The concept of an objective (frame indifferent) stress rate is introduced. The behavior of several objective stress rates in a material undergoing simple extension is discussed. The response of a hypoelastic material in simple shear, in both the elastic and elatic/plastic regimes, is evaluated, and it is concluded that for materials with low yield strength, such as metals and geologic materials, use of the Jaumann stress rate is justified. Keywords: Stress Rates; Objectivity; Constitutive Relations; Frame Indifference; Plasticity.